There seems to be some confusion about exactly how the Volkswagen
Syncro/Audi Quattro I system works. This document aims to set that record
straight, and may or may not succeed, but it tries very hard, so give it
some credit : ) This document applies to the following cars, and probably
a few others that I've forgotten:
Audi 4000 Quattro
Audi 5000 Quattro
Volkswagen Quantum Syncro (all years)
Audi Turbo Quattro Coupe, aka ur-q, TQC
This document does NOT apply to the Vanagon Syncro, which has a completely
and utterly different viscous-coupling system.

Differentials

These cars have three differentials: a center, rear, and a front. The
center diff divides power between the front and rear diffs. The front diff
divides power between the front wheels, and the rear diff, predictably,
divides power between the rear wheels. These diffs are all conventional
open diffs, which means that they split torque evenly. Under normal
circumstances, all four wheels will spin at approximately the same rate,
all powered. However, say if the right rear wheel of the car lifts off the
ground, the center and rear diffs will have one output shaft that is
really easy to spin, and the front diff will never see any motion at all
(although it will get the same amount of torque as the rear diff, but it
won't spin anything - this is kindof confusing, but if you think about it
for a while, it makes sense). The upshot of this is that only that wheel
that is off the ground will
spin, since it takes less torque to spin that wheel than it does to move
the other wheels and move the car.
This is what's bad about conventional
diffs, and it's why when a normal car gets stuck in a ditch, only one
wheel spins and it's the "wrong" one.

Differential locks

This is where differential locks come in. Without them, the Quattro
would be nothing really special. When a diff is locked, both output shafts
are forced to turn at the same speed, with up to potentially 0/100% torque
split, in theory (except that it always takes some torque to turn wheels,
even when they are off the ground). So, if the center diff is locked
(knob pulled out one notch, one green light lit), one front wheel and one
rear wheel, at least, will be forced to spin. With the rear diff locked as
well (knob pulled out all the way, both green lights on), both rear wheels
will be forced to turn at the same rate as well, and the car becomes
effectively 3-wheel drive under any circumstances. This isn't true AWD,
one could argue, but it's certainly better than conventional "4wd". (Just
to set the record straight, when you put a non traction-control or
anything new and fancy equipped truck/SUV/Jeep/whatever in "4wd", it
becomes what an Audi Quattro I is with the center diff locked). The
first Audi to have "true" AWD is the new Quattro IV's, which have a
Torsen center diff and electronic traction control which utilizes the
brakes front and rear.

Problems with diff locks

So why not leave the diffs locked all the time, you say? Well, your
front wheels describe a larger arc than your rear wheels when turning, and
the outside wheels turn faster than the inside ones. So when you have your
diffs locked, the tires and road surface have to scrub off this
difference, causing "hopping", and lots of wear and tear on tires, diffs,
and much of the steering and suspension system. This problem, and the fact
that your average consumer has no idea how Quattro I works or how to use
it, is why Audi switched to Quattro II with the 80/90 and 100/200
Quattros, which has a torque-sensing Torsen center differential.